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U2L1k.txt
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#
# File: content-mit-8370x-subtitles/U2L1k.txt
#
# Captions for course module
#
# This file has 119 caption lines.
#
# Do not add or delete any lines. If there is text missing at the end, please add it to the last line.
#
#----------------------------------------
So I think I might have time to cover a really neat quantum
protocol called Vaidman bomb detection.
Yeah.
OK, and here, we're actually going
to have to draw beam splitters and quantum optical tables.
So the basic idea is you have a bomb.
And you have a whole bunch of these bombs,
and you'd like to test them, whether they are actually
defective or not.
So the bomb has a little fuse on it.
And the fuse is so sensitive, if you shine one photon on it,
it explodes.
One photon on fuse, bomb explodes.
So of course, you keep these bombs in the dark.
And what you would like to do is you would like to see--
and some bombs are missing fuses.
Some bombs are missing fuses.
So you would like to make sure these bombs actually
have fuses.
But you want to check to see whether they
have fuses without exploding.
But of course, if you look at the fuse, it explodes.
So what do you do?
Well, I am going to--
what we're going to do is we're going to set up a--
no, two half-silvered mirrors and a source of photons.
And this is a plane mirror.
And this is a plane mirror.
So this is an interferometer.
And we adjust it.
Adjust interferometer so that if there's
nothing in the path, nothing in path,
everything goes to this detector one, detector two.
All photons go to detector one.
So I mean you can model this as basically this
is a hadamard gate.
And this is another hadamard gate.
And when you multiply them, everything
goes to this detector.
And now, what we're going to do is
we're going to put a bomb here with its fuse over the path.
Well, assuming it has a fuse, the fuse
will be over the path of this photon.
No bomb, 100% detector one.
Suppose there is a bomb.
Well, what happens is a photon goes through
with 50% probability, it goes this way
and explodes the bomb--
50% probability bomb explodes.
In which case, we actually don't see any signal
at the detectors.
If the other 50%, it goes this way, and it goes up this way,
but now, there's no interfering ray coming from this path,
so the photon goes this way with 50% probability and this way
with 50% probability--
25% detector one, 25% detector two.
So if the bomb is defective, detector one
is the one that triggered.
If the bomb has a fuse, 25% of the time detector two
is triggered.
So whenever we get detector two, we know it's a good bomb.
And we know that there is a fuse in it.
And we have not looked at the fuse.
So of course, this is something you cannot do classically.
If you have a bomb that has a fuse on it,
and you want to check whether there's a fuse,
you have to look at the fuse somehow.
And if you look at the fuse, the bomb explodes.
So this is a way of getting some bombs out
or some bombs which we know have fuses out
without exploding them all.
And if you want, you can set up a much more complicated
optical experiment, which explodes the bomb not
with 50% probability, but with maybe 1%
probability or 0.01% probability.
So you can set up a much more complicated optical experiment,
which almost always detects good bombs.
But that's more complicated.
And I'm not going to go through it in this class.
OK, good.
Yeah?
Can you make a device which has sort of an arbitrarily
small, as in you could make this interferometer as complicated
as you want and you can get whatever
probability of the bomb exploding as you want,
basically?
That's right.
But you can't set it all the way to zero.
There has to be some probability the bomb explodes.
But well, basically, the idea is that you
have mirrors so that the photon goes up and down here
many, many times.
And the more times it goes up and down,
the lower probability you can get it of having an actual bomb
explode.
But I guess to get zero, you would
have to have it go up and down infinitely many times.
And that doesn't work.
So that's the basic idea for reducing this probability.
Any other questions?